Two pyridinecarboxamide dicyanidecobalt(III) building blocks and two mononuclear seven-coordinated macrocycle manganese(II) compounds have been rationally selected to assemble cyanide-bridged heterobimetallic complexes, resulting in three cyanide-bridged $Co^{III}-Mn^{II}$ complexes. Single X-ray diffraction analysis show that these complexes ${[Mn(L^1)][Co(bpb)]}ClO_4{cdot}CH_3OH{cdot}0.5H_2O$ ($mathbf{1}$), ${[Mn(L^2)][Co(bpb)]}ClO_4{cdot}0.5CH_3OH$ ($mathbf{2}$) and ${[Mn(L^1)][Co(bpb)]}ClO_4{cdot}H_2O$ ($mathbf{3}$) ($L^1$ = 3,6-diazaoctane-1,8-diamine, $L^2$ = 3,6-dioxaoctano-1,8-diamine; $bpb2^{2-}$ = 1,2-bis(pyridine-2-carboxamido)benzenate, $bpmb2^{2-}$ = 1,2-bis(pyridine-2-carboxamido)-4-methyl-benzenate) all present predictable one-dimensional single chain structures. The molecular structures of these one-dimensional complexes consists of alternating units of $[Mn(L)]^{2+}$ ($L=L^1$ or $L^2$) and $[Co(L^{prime})(CN)2]^-$ ($L^{prime}=bpb2^{2-}$, or $bpmb2^{2-}$), forming a cyanide-bridged cationic polymeric chain with free $ClO_4{^-}$ as the balance anion. The coordination geometry of manganese(II) ion in the three one-dimensional complexes is a slightly distorted pentagonal-bipyrimidal with two cyanide nitrogen atoms at the trans positions and $N_5$ or $N_3O_2$ coordinating mode at the equatorial plane from ligand $L^1$ or $L^2$. Investigation over magnetic properties of these complexes reveals that the very weak magnetic coupling between neighboring Mn(II) ions connected by the diamagnetic dicyanidecobalt(III) building block. A best-fit to the magnetic susceptibility of complex ${mathbf}{1}$ leads to the magnetic coupling constants $J=-0.084(3)cm^{-1}$.